Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-x-2y &= -7 \\ 7x+2y &= -7\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $6x = -14$ Divide both sides by $6$ and reduce as necessary. $x = -\dfrac{7}{3}$ Substitute $-\dfrac{7}{3}$ for $x$ in the top equation. $+ \dfrac{7}{3}-2y = -7$ $\dfrac{7}{3}-2y = -7$ $-2y = -\dfrac{28}{3}$ $y = \dfrac{14}{3}$ The solution is $\enspace x = -\dfrac{7}{3}, \enspace y = \dfrac{14}{3}$.